FR2536541A1 - Simplified spectral analysis system using phases - Google Patents

Abstract

The system has at its input a Cartesian-to-polar coordinate transformer RP receiving the binary variables Xn and Yn representing the real and imaginary parts respectively of the nth sample of the received signal. This is followed by a binary rearrangement device RB supplying a binary number PHI n = RnSnTn "proportional" to the phase of the received signal. Phase combinations of the type e<j PHI >n.e<-2 pi j>kn/N occurring in the expression for the discrete Fourier transform of dimension N are then produced by a set of standard binary subtractors AD0 - AD7. After a polar-to-Cartesian coordinate transformation in polar-to-Cartesian coordinate transformers in coordinate transformers PR0 - PR7, the signals supplied are summed in adders SIGMA 0 - SIGMA 7. The modulus ¦Ai¦ of the spectral lines supplied can then be calculated by simplified modulus calculators CM0 - CM7. The system includes only standard logic devices. Application to Fourier transform calculators.

Description

The invention relates to a system for performing the spectral analysis of a signal by phase exploitation.

In pulse Doppler radars, signal processing operations are increasingly performed by digital techniques. They offer the advantage, over analog techniques, of greater fidelity and above all greater flexibility of operation. It is thus possible, in the context of digital processing, to adapt the processing circuits to different transmission modes by re-tuning the filters in a way. It is thus possible to reduce the necessary nursery volume by using it in timeshare. This flexibility of operation is practically not accessible to analog circuits.

However, digital signal processing units are often complex and costly. Technical and technological progress remains to be made to achieve digital functions, specialized in the form of monolithic boxes, whether or not they are programmable. In particular, devices capable of performing multiplications on two binary numbers are rare and expensive.

Some of these pulse Doppler radars include a specialized operator, called a "spectrum analyzer", intended to classify the signals from their apparent Doppler frequency, the aim of this operation being the classification of the various targets; by their radial speed.As part of a radar has several recurrence frequencies, for example, the comparison of different; Doppler frequency shifts make it possible to resolve certain ambiguities in speed
This spectral analysis can be carried out numerically by various systems which can use a certain number of classical algorithms, more or less compact and complicated, such as the so-called discrete Fourier transform algorithms, or TF8i, Q ecz3e the transform algorithms of Fast Fourier (FFR), whether root 2, root 4, or Winograd, or like recursive algorithms.

All these algorithms start from the n-dimensional discrete Tourier transform of the complex sequence {an}, with an = O a N-1, defined by the complex sequence

However, in all the systems used, such as for example in the system described in French patent application No. 80 13162 filed on June 13, 1980, in the name of the applicant and entitled: "Calculation module and calculation device using it for the determination of the discrete Fourier transform of a series of samples ", one uses complex numbers, such the numbers a of the complex series {an}, in the form an nn +
The qualities of an algorithm are then judged by the number of additions and especially by the number of necessary multiplications. However, it is much simpler to carry out multiplications of complex numbers when eernrsi are given in the form a = pn effn. But, in this case, it is the additions that prove difficult to achieve.

k variant de O a N-1, d'une suite complexe d'entrée {an, an = xn + jyn} et recevant successivement des couples de variables binaires, Xn et Yn, représentant respectivement la partie réelle xn et la partie imaginaire yn de la suite d'entrée {an an constituée par les échantillons successifs du signal à analyser, mais qui n'utilise que des circuits logiques fondamentaux de grande diffusion.We can therefore think of carrying out a rectangular, linear transformation before carrying out one or more multiplications, then carrying out the inverse transformation before carrying out one or more additions Unfortunately, the simplification provided by this type of multiplication is compensated by the additional complication brought by performing all these coordinate transformations
Thus, the object of the present invention is to describe a simplified spectral analysis system making it possible to obtain, simultaneously, on its N outputs, the N lines of the discrete Fourier transform of dimension N,

k variant from O to N-1, from a complex input sequence {an, an = xn + jyn} and successively receiving pairs of binary variables, Xn and Yn, representing respectively the real part xn and the imaginary part yn of the input sequence {an an consisting of the successive samples of the signal to be analyzed, but which only uses fundamental logic circuits of wide distribution.

According to the invention, the simplified spectral analysis system comprises, at the input, a cascade assembly, rectangular-polar coordinate transformer and transcoder receiving the digitized components X and Y, samples of the signal to be analyzed and
nn supplying, with N identical channels, the digitized values #n of the phase n of the samples of this signal. These N channels are each composed of a phase rotator constituted by a binary adder-subtractor carrying out the binary subtractions Hk, n = in - N * Fk or the
binary additions H = # + N # G1, representing the phase rotation #n - 2 # Kn that it is necessary to perform on each input vector (xn,), of phase n. In these expressions, N # is the binary value of the index n and the uppercase letters, indexed, correspond to binary values. These phase rotators are followed by a polar-rectangular coordinate converter providing ,, from the phases Hk, n received from the phase rotators, the binary components Xk, n and Yk, n, of the unit vector represented by the complex number

These channels then include a double adder
performing the summation of the N components in quadrature, received successively
sively, then a modulus calculator receiving the binary output variables h and EYk supplied by the double summers and supplying the binary variable representing the modulus z qc of the line of index k. The N phase rotators receive on the other hand, on their second input, the phase rotation angles associated with the channel, of index k, considered and with the sample number, of index n, received. These phase rotation angles are provided by N devices for generating these phases, each being associated with a phase rotator.

The invention will be better understood and other characteristics will appear with the aid of the description below and the accompanying drawings in which - FIG. I represents a diagram of a spectral analysis device.
according to the invention; - figure 2 represents the rectangular coordinate transformer -
polar used in this analysis device; - Figure 3 shows a series of four graphs allowing.

explain the operation of this coordinate transformer; - figure 4 represents a fifth graph making it possible to explain the
working of this coordinate transformer; - figure 5 shows the binary rearranging device used
in this analysis device; - Figure 6 represents a graph making it possible to understand the function
development of the binary rearrangement device used in this analysis device; ; FIG. 7 represents a graph making it possible to explain the function
development of transformers with polar-rectangular coordinates,
used in this analysis device; Figure 8 shows a detailed part of Figure 1; - Figure 9 shows a variant of the same detailed part of
figure 1; - Figure 10 shows a diagram of a spectral analysis device
in linear mode, according to the present invention; and - Figures 11 and 12 represent the amplitude-frequency responses of
the first analysis output for two types of output integrators
and as part of an analysis device, such as the one shown in
figure 10.

The diagram of the spectral analysis device by phase exploitation, according to the present invention, is shown in FIG. 1.

it comprises a rectangular-pole coordinate transformer RP, receiving the binary variables X and Y coded on p binary elements
nn and respectively representing the real part xn and the imaginary part yn of the sample, of the received signal index n. This coordinate transformer supplies the binary elements An, Bn, Cn and Dn corresponding to the phase of this received signal. These binary elements are supplied to a transcoder RB performing a binary reorganization and supplying binary elements Rn S and T such as the number
nn binary RST n is "proportional" to the phase of the signal received, the axis
nn real being taken as the origin of the phases. The system described here is a spectrum analyzer with eight binary elements (N = 8), corresponding to the eight samples an = xn + jyn received successively on the input of the coordinate transformer RP and which therefore simultaneously provides eight distinct lines or channels. From the base 8 system described, it is possible to extrapolate to systems working on higher bases like 16 or 32.

que l'on trouve dans l'expression de la transformée de Fourier discrète de dimension N

It is therefore a question here of calculating the modulus on n and the phase fn of the elements an of the complex input sequence {an}, these being received in the form an = xn + jyn. This module and this phase will then be used to carry out the multiplications of the type

that we find in the expression of the discrete Fourier transform of dimension N

We can achieve this transformation in a simple way if we accept a large digitization step. From the choice of a system working on the polar coordinates p and #, it is therefore at the level of the rectangular-polar and polar-rectangular transformations that the solution according to the present invention achieves the simplification of the system.

This simplification naturally entails a loss of information, but this can be amply justified for certain types of equipment having regard to its low production cost.

The operation of these first two stages will now be explained with the aid of Figures 2 to 6. As shown in Figure 3, the complex plane is divided into eight domains by four binary comparators C1, C2, C3 and C4 which make up the rectangular-polar coordinate transformer RP shown in figures t and 2. These comparators respectively carry out the following operations: A = 1 for Y # 0; B = 1 for Y # X; C = 1 for X # 0 and D - 1 for X # -Y. As represented in FIG. 4, each domain, corresponding to one eighth of the complex plane, is therefore associated with a binary number ABCD with four binary elements. For each sample (.X Yn) received, this coordinate transformer provides four binary elements An , Bn, Cn, D representative of the + phase of this
n sample.

The transcoder RB, shown in Figures I and 5, receives: these four binary elements A, B, C and D and transforms this binary number ABCD into a new binary number = EST, with three binary elements R, S and T, associated to the same portion of the complex plane but such that it is proportional "to the phase # of the sample considered of the received signal. For eight successive digitized samples (X, Yn), n = 0 to 7, this transcoder will provide therefore eight successive binary numbers #n = RnSnTn representing the phases #n of these samples it can be constituted simply by a read only memory or ROM memory.

k variant de O à 7 entrant dans l'expression de la transformée de Fourier discrète de dimension 8,

puisqu'il suffit ici de calculer les phases hk,n = #n - 2rk n, pour les huit valeurs possibles de k
il s'agit donc de faire effectuer au vecteur signal d'indice 0 (x0, y0) huit rotations de phase identiquement nulles, au vecteur signal d'indice 1 (x1, Y1), de phase #1, les rotations de phase f0 = 0, f1 = 2# 1, f2 = 2# 2, ..., fk = 2# k, ..., f7 = 2# 7 dans le
8 8 8 8 sens négatif, au vecteur signal d'indice 2 (x2, Y2) de phase #2, les rotations de phase 2f0 = 0, 2f1, 2f2, ..., 2fk, ..., 2f7, dans le sens négatif, etc.. Parallèlement à la création des codes binaires utilisés pour décrire les phases #n = RnSnTn des échantillons du signal, huit valeurs de rotation fondamentales de phase sont donc crées F0, F1, F2, ..., F Fk ... et F7, valant 0,1, 2, ...9 7. Elles permettent d'obtenir les phases cherchées (hk,n 0 #n - 2#k n) par soustraction à chaque
8 vecteur siganl, de phase #n = RnSnTn, d'un multiple de chacune de ces rotations de phase fondamentales.On obtient Hk,n = n - N#Fk, ou N# est la valeur en binaire de l'indice n. Ces décréments de phase F et les décrements de phase complémentaires Gk s'écrivent en binaire
F0 = 000 G0 = 000 = G8
F1 = 001 ci = 111
F2 = 010 G2 = 110
F3 = 011 G3 = 101
F4 = 100 G4 = 100
Es = 101 G5 = 011
F6 = 110 G6 = 010
F7 = III G7 = 001.As shown in Figure 1, phase #n of the exchan-
The index n of the signal is supplied to each of the binary subtractors of a bank of binary subtractors or phase rotators ADO to AD7, allowing eight rotations to be carried out simultaneously
This battery of subtractors makes it possible to calculate in a simple way the eight products of the type

k varying from 0 to 7 entering the expression of the discrete Fourier transform of dimension 8,

since it suffices here to calculate the phases hk, n = #n - 2rk n, for the eight possible values of k
it is therefore a matter of making the signal vector of index 0 (x0, y0) perform eight identically zero phase rotations, to the signal vector of index 1 (x1, Y1), of phase # 1, the phase rotations f0 = 0, f1 = 2 # 1, f2 = 2 # 2, ..., fk = 2 # k, ..., f7 = 2 # 7 in the
8 8 8 8 negative direction, at the vector signal of index 2 (x2, Y2) of phase # 2, the phase rotations 2f0 = 0, 2f1, 2f2, ..., 2fk, ..., 2f7, in the negative direction, etc. In parallel with the creation of the binary codes used to describe the phases #n = RnSnTn of the samples of the signal, eight fundamental phase rotation values are therefore created F0, F1, F2, ..., F Fk. .. and F7, equal to 0.1, 2, ... 9 7. They make it possible to obtain the sought phases (hk, n 0 #n - 2 # kn) by subtraction at each
8 vector siganl, of phase #n = RnSnTn, of a multiple of each of these fundamental phase rotations. We obtain Hk, n = n - N # Fk, where N # is the binary value of the index n. These phase decrements F and the complementary phase decrements Gk are written in binary
F0 = 000 G0 = 000 = G8
F1 = 001 ci = 111
F2 = 010 G2 = 110
F3 = 011 G3 = 101
F4 = 100 G4 = 100
Es = 101 G5 = 011
F6 = 110 G6 = 010
F7 = III G7 = 001.

These complementary phase decrements Gk, or phase increments, make it possible to replace the subtractors ADO to AD7 by adders ADO 'to AD7'. The phases sought are then written in binary: Hk, n = # + N # Gk.

In FIG. 1, this battery of subtractors ADO to AD7 is shown. Each of these tractor sounds receives, on the one hand, the phase #n = RnSnTn of the nth sample of the signal vector and, on the other hand, one of the values, N # F0 to N * F7, obtained from one of the eight core values, F0 to F7, previously defined.

Figure 8 shows, on the one hand, part of figure 1 with the subtractors ADO, ADI, AD2, ... and, on the other hand, the devices, R1, Si and R2, S2, allowing to get, at every signal
clock and from the fundamental rotations previously defined,
the phase values NOFO, N'F1, NF2. # # which must be subtracted from the input vector during the nth clock signal The first subtracter ADO directly receives the fundamental phase value F0 = N # F0, i.e. F0 = 000 The second subtracter AD1 receives the phase value N # F1, obtained from the fundamental value F1 and supplied by the first adder Si This first adder SI receives on its first input the fundamental phase value F1 and, on its second input, the output of a shift register R1 This shift register itself receives on its input the output signal of this first adder.With each pulse of the clock signal R acting on the shift register, the adder S1 provides on its output a new sum, incremented by binary number F1. If the register R1 is reset to zero at the first clock pulse, for the reception of the sample of index 0, and the first input of the adder S1 inhibited, the first value supplied to the subtracter ADI will be identically zero. Then, the second value will be equal to F1, the third value will be equal to 2F1, and at the instant of appearance of the sample of index n, the value supplied to the subtracter AD1 will indeed be N4F1. In the same way, the device R25 S2, consisting of a second shift register R2 and a second adder 52, will supply the sub-tractor AD2, successively, with the binary numbers 0,
F2, 2F2, ..., N # F2.

In FIG. 9 is shown a variant of the device of FIG. I with the use of adders ADO1 to AD7 'instead of subtractors ADO to AD7. The first adder ADO 'should then receive the phase increment Go = NoGo, i.e. Go = 000, the second adder AD1' should receive the phase increment NOG1 from a register-adder unit R1'-S1 'and the adder ADK 'of index k must receive the phase increment N # Gk of a registreadder set RK'-SK'.

As represented in FIG. 1, each of the subtractors, ADO to AD7, supplies its output binary number Ho n to H7, n to a coordinate converter, PRO to PR7. The coordinate converter of index k receives the three-bit binary numbers Hk, n proportional to a phase angle and outputs the component pairs
orthogonal (Xk, n, Yk, n) The way in which this conversion is carried out,
from polar coordinates to rectangular coordinates, can be
understood by referring to figure 7 and the table below

Numbering <SEP> Hk, n <SEP> Xk, n <SEP> Yk, n
<tb><SEP> decimal
<tb><SEP> O <SEP> 000 <SEP> + <SEP> O <SEP>
<tb><SEP> 001 <SEP> + <SEP> 1 <SEP> + <SEP> 1
<tb><SEP> 2 <SEP> 010 <SEP> O <SEP> + <SEP> 1 <SEP> 91 <SEP>
<tb> 3 <SEP> 011 <SEP> ~ <SEP><SEP> 1
<tb><SEP> 4 <SEP> 100 <SEP> -1 <SEP> O <SEP>
<tb><SEP> 5 <SEP> 101 <SEP> - <SEP> I <SEP> -1 <SEP>
<tb> 6 <SEP> 110 <SEP> O <SEP> - <SEP>
<tb> 7 <SEP> 111 <SEP> + <SEP><SEP> 1 <SEP> - <SEP> 1 <SEP>
<tb>
All the vectors, whose binary phase code is 000 and which are therefore included in the first eighth of a plane, are associated with a zero phase angle # = O and will have X = + 1 as abscissa and Y = O for ordinate. All the vectors, whose binary phase code is 001 and which are therefore included in the second eighth of a plane, are associated with a phase angle of # and will have for abscissa X = +1 and for
8 ordinate Y + 1 ... etc.

Spectral analysis at this stage is not yet complete. It is necessary to integrate the samples of each of the pairs of outputs of the coordinate converters PRO to PR7. This operation determines the bandwidth of each filter. The first coordinate converter PRO is followed by a double integrator # 0 receiving the sequence X0, n and the sequence Y0, n of binary numbers and providing the sums # X0 and # Y0. The second PRI coordinate converter is followed by a double integrator Si receiving the sequence X1 n and the sequence Y1, n of binary numbers and providing the sums # X1 and SY - The kth coordinate converter PRK is followed by a double integrator #K receiving the sequence X1, k and the sequence Y1, k of binary numbers and providing the sums #Xk and #Yk.

- une intégration transversale récursive du deuxième ordre qui procure
des flancs plus raides et qui est représentée par la transmittance en z suivante

At this stage, several types of integrations can be imagined, for example - a transverse integration of eight unweighted samples
realizing the following transisttance in z
I1 (z) = 1 + z-1 + z-2 + z-3 + z-4 + z-6 + z-7
whose gain is equal to 8, corresponding to three binary elements
additional that will have to be included in the calculations above the
strong weights of the entrance; you will have to drop the element
least significant binary, as we will see later; or a transverse integration of eight successive weighted samples
performing the following z-transmittance:
I2 (z) = b0 + b1z-1 + b2z-2 + b3z-3 + b4z-4 + b5z-5 + b6z-6
-7
+ b7 z
in which the weighting coefficients are chosen in such a way
simple and for which it will also be necessary to envisage, according to the equal gain
to the sum of the coefficients b0 to b7, two or three binary elements
additional above the heavy weights of the entrance; or a first order recursive transverse integration represented
by the following z-transmittance

- a second order recursive transversal integration which provides
steeper flanks and which is represented by the following z-transmittance

All of these types of integrators are well known. They are given here by way of example and do not form part of the invention.

ou ##Xk# et ##Yk# représentent respectivement les valeurs absolues: des nombres E et SYk. The spectral analysis device is completed by output module computers, NO to M7, each placed at the output of one of the double integrators, 50 to S7, and receiving therefrom the components #Xk and SYk supplied. Each spectral component is here "detected" by a simplified module operator of the type:

where ## Xk # and ## Yk # respectively represent the absolute values: numbers E and SYk.

These module calculators are made up of a single adder not receiving the sign binary elements and not providing its least significant binary element so as to perform a division by two. This division can also be carried out by removing the least significant bit from the input variables SXk and #Yk at the input (figure 10).

From the base 8 system, it is possible to extrapolate to systems working on larger dimensions, for example 16 or 32. A base 16 solution can be obtained - by shifting the eight filters by an angle # = 16 by a translation
frequency obtained by its recursive phase rotation system; - by jointly reducing the bandwidth of integrators in
a ratio 2 (transversal integration of order 16 or integration
recursive with different coefficients).

It is possible to realize a more complete version of this spectral analysis system. This new version keeps the amplitude information of the signal received unlike the version previously described in which, for the sake of simplification, each sample received was coded only in phase.

FIG. 10 represents the diagram of such an analysis device using the on module of the input signal: When the spectral analysis is desired in a linear mode, it is necessary to reconstruct the amplitude of the signal using this module of the input signal before integration. This nodule is calculated by a CM module calculator, in the input format, from an approximate formula of the type

This module calculator therefore receives the digitized samples of the input signal in the form of binary variables X and Y
nn which are transmitted to it without their binary bookmark element provides the approximate binary value M of the module p. it is made up only
nn of a binary adder.

est toujours reallse comme dans le cas de la figure I en effectuant tout d'abord les opérations sur les phases par le transformateur de coordonnées rectangulairepolaire RP, le dispositif de réarrangment binaire RB et la batterie d'additionneurs ADO' à AD7, ou la batterie de soustracteurs ADO à AD7 selon la variante choisie (figures 8 et 9).The computation of the discrete Fourier transform of dimension N

is always carried out as in the case of figure I by first performing the operations on the phases by the rectangularpolar coordinate transformer RP, the binary rearrangement device RB and the battery of adders ADO 'to AD7, or the battery of subtractors ADO to AD7 according to the chosen variant (figures 8 and 9).

The exponential operators, of phases #n - 2 # kn, are
N each converted by the polar-to-rectangular converters, PRO to
PR7, in a complex number of unit modulus, coded according to the diagram of FIG. 7. The approximate modulus M of the sample considered is then
n introduced on each of the components X, n Y # supplied by this battery of polar-rectangular converters. Those are. the double binary multipliers Mû to M7 which are used to reinject the approximate module M into each of the channels. These double multipliers
n operating on the two components Xk, n and Yk, n supplied by the corresponding coordinate transformer PRK. The components, in linear mode, supplied Mn Xk, n and Mn Yk, n are then, as in the case of figure 1 , integrated in summers 50 to S79 then a module calculation is carried out by the module computers CMO to CM7
If the X and Y samples of the input signal are digitized
nn on p binary elements, the approximate modulus Mn will be given with p-1 binary elements and, the components Xk, n and Yk, n being given on two binary elements including one of sign, the components in linear mode Mn Xk, n and Mn Yk, n will therefore have p binary elements
These components are obviously obtained by conventional binary multipliers able to receive input variables coded on respectively 2 and p-1 binary elements. The integration of the components obtained provides the quadrature components of the lines in the form of binary variables with p + 3 binary elements, p + 2 binary elements being transmitted to the module calculator to perform a division by 2 at the input. spectral obtained is detected by a module calculator CMO to CM7, providing the approximate modules # Ak #
FIG. 11 represents the amplitude-frequency response of the spectral analysis device represented in FIG. 10, in the case of a transverse integration of eight successive unweighted samples. the signal represented in solid line corresponds to the output of the voice of index zero supplying the module # A0 # of the first line.

The amplitude of this line is plotted on the ordinate, in decibels, and the normalized frequency on the abscissa. The normalized limit frequency or frequency i corresponds to the recurrence frequency. The signals represented by dotted lines represent the different responses of the channels of indices 1 to N-i. In order not to weigh down the figure, the upper part of the main lobe supplied by these channels has been shown here. Each of these main lobes supplied by these different channels are offset from one another by one eighth of the normalized frequency.

FIG. 12 represents the amplitude-frequency response of the spectral analysis device represented in FIG. 10 in the case
of a first order recursive transverse integration The signal
shown in solid line also corresponds to the output of the first
channel providing the # A0 # module of the first line. The signals shown in dotted lines correspond to the outputs of channels 1 to N 1.

These responses are reported here under the same conditions as those in Figure 11.

It can be seen that, despite the successive approximations9, the conventional shapes of the signals supplied by known spectra analyzers are indeed obtained.

Although the present invention has been described in the context of particular embodiments, it is clear that it is not limited to said examples and that it is susceptible of modifications or variations without going beyond its scope. For example, since the number of lines or channels provided can be between different from 8, the number of binary compo rators, constituting the rectangular-polar coordinate converter, could be modified to reduce or increase the digitization step of the phases of the signal.

Claims (7)

1. Simplified spectral analysis system making it possible to obtain, simultaneously on its N outputs, the N lines of the transform of Discrete Fourier of dimension N,

k varying from 0 to N-1, from a complex input sequence {a, a = x + iy} and successively receiving pairs of binary variables K and Y representing nn respectively the real part xn and the imaginary part yn of the input sequence {an} constituted by the successive samples of the signal to be analyzed, characterized in that it comprises: at the input a transformer cascade set of rectangular coordinates -polar (RP) and transcoder) (RB), receiving the digitized components, Xn and Yn, of the samples of the signal to be analyzed and providing, at N identical channels, the digitized values w #n of the phase #n of the samples of this signal , in that these N channels are each composed of a phase rotator (ADO to AD7 or ADO 'to AD7') constituted by a binary adder-subtractor carrying out the binary subtractions Hk, n = #n - N + Fk or the binary additions Hk, n = #n + N + Gk representing the phase rotation #n - 2 # kn that it is necessary to perform on each vector Input N xn, Yn, of phase #n, of a polar-rectangular coordinate converter (PRO to PR7) supplying, from the phases Hk, na received, from the phase rotators, the binary components Xk;> and Yk, n of the unit vector represented by the complex number

of one. double adder (50 to 57) carrying out the summation of the N components in quadrature received successively and from a module calculator (CMO to CM7) receiving the binary output variables #Xk and #Yk supplied by the double summers and providing the variable binary representing the modulus # Ak # of the line Ak of index k, and in that these N phase rotators receive on the other hand, on their second input, the phase rotation angles associated with the channel, of index k, considered and at the sample number, of index n, received, these phase rotation angles being provided by devices for generating these phases (Ri-S1 to R7-S7 or R1'-S1 'to R7' -S7 '), each associated with a phase rotator (ADO to AD7 or ADO 'to AD7'). 2. Simplified spectral analysis system according to claim cation 1, characterized in that the binary components of the type Xk, n and Yk, n, provided by the N rectangular polar converters (PRO to PR7), are provided directly on the respective inputs of the corresponding summers (#O to S7). 3. Simplified spectral analysis system according to claim 1, characterized in that it further comprises a module calculator (CM) also receiving the input binary variables Xn and Yn and providing an approximate binary value Mn of the. modulus #n of the sample considered at each of N double multipliers (MO to M7) operating on each of the binary components Xk, n and Yk, n supplied by the polar-rectangular coordinate converters (PRO to PR7), each of these double multipliers being inserted in each of the identical channels between the coordinate converters (PRO to PR7) and the summers w (#O to # 7), and supplying the latter with the binary components in Linear mode Mn Xk, n and Mn Yk, n . 4. SimpIiîé spectral analysis system according to any one of claims i to 3, characterized in that the rectangular-polar coordinate converter (RF) consists of four binary comparators (C1, C2, C3, C4) each receiving the digitized components K and Y of the signal to be analyzed, the first (CE) providing the n n binary variable An verifying the relation An = 1 for Yn # 0, the second (C2) providing the binary variable B verifying the n relation Bn = 1 for Yn # Xn, the third (C3) providing the binary variable Cn verifying the relation Cn = 1 for Xn # 0, and the fourth (C4) providing the binary variable D verifying the relation 9 = I n n for X # 5 simplified spectral analysis system according to any one of claims 1 to 4, characterized in that the transcoder (RB) consists of a read only memory, associating with the binary variable A, Bn, Cn, Dn received, a new binary variable #n = RnSnTn proportionally representing the phase #n of the signal received, the real axis being taken as the origin of the phases. 6. Simplified spectral analysis system according to any one of claims 1 to 5, characterized in that the polar-rectangular coordinate converters (PRO to PR7), receiving from their phase rotator (ADO to AD7 or ADO 'to AD7 ') the binary quantities representing the angels of phase hk, n = #n - 2 # nk, are memories N dead bodies which carry out this polar-rectangular conversion so that the binary components supplied take only three possible values +1, 1 and O. 7 Simplified spectral analysis system according to any one of claims 1 to 6, characterized in that the first adder-subtractor (ADO or ADO ') receives on its second input a constantly zero binary variable F0 or Go and in that each of the other adders-subtractors (ADI to AD7 or ADI 'to AD7') receives on its second input a binary variable N Fk or NGk supplied by its device for generating phase rotation angles (RK-SK or this device comprising an adder ( SK or SK ') and a shift register (PK or RK'), the adder (5K or SK ') receiving, on its first input, the fundamental rotation Fk. Or Gk of index k, in the form of a binary word of three binary elements, and, on its second input, the output of the shift register (RK or RK ') and providing on its output the binary variable NtFk or N Gk, where N is the binary value of the index n of the treated sample.